# Continuous Record Asymptotics for Change-Point Models

*Alessandro Casini* () and
*Pierre Perron*

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Alessandro Casini: University of Rome Tor Vergata

No WP2020-013, Boston University - Department of Economics - Working Papers Series from Boston University - Department of Economics

**Abstract:**
For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a fixed time horizon [0, N] , and let T â†’ âˆž with h â†“ 0 while keeping the time span N fixed. We impose very mild regularity conditions on an underlying continuous-time model assumed to generate the data. We consider the least-squares estimate of the break date and establish consistency and convergence rate. We provide a limit theory for shrinking magnitudes of shifts and locally increasing variances. The asymptotic distribution corresponds to the location of the extremum of a function of the quadratic variation of the regressors and of a Gaussian centered martingale process over a certain time interval. We can account for the asymmetric informational content provided by the pre- and post-break regimes and show how the location of the break and shift magnitude are key ingredients in shaping the distribution. We consider a feasible version based on plug-in estimates, which provides a very good approximation to the finite sample distribution. We use the concept of Highest Density Region to construct confidence sets. Overall, our method is reliable and delivers accurate coverage probabilities and relatively short average length of the confidence sets. Importantly, it does so irrespective of the size of the break.

**Keywords:** Asymptotic distribution; break date; change-point; highest density region; semimartingale (search for similar items in EconPapers)

**JEL-codes:** C10 C12 C22 (search for similar items in EconPapers)

**Pages:** 94 pages

**Date:** 2020-03

**New Economics Papers:** this item is included in nep-ecm, nep-ets and nep-ore

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http://www.bu.edu/econ/files/2020/05/CASINI_PERRON_Single_Break_CR.pdf

**Related works:**

Working Paper: Continuous Record Asymptotics for Change-Points Models (2021)

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**Persistent link:** https://EconPapers.repec.org/RePEc:bos:wpaper:wp2020-013

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